NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Closed-Form Likelihood Expansions for Multivariate Diffusions

Yacine Ait-Sahalia

NBER Working Paper No. 8956
Issued in May 2002
NBER Program(s):   AP

This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions. The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis. Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for discretely sampled multivariate diffusions. Examples of interest in financial econometrics are included.

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Document Object Identifier (DOI): 10.3386/w8956

Published: Ait-Sahalia, Yacine. "Closed-Form Likelihood Expansions for Multivariate Diffusions," Annals of Statistics, 2008, 36, 906-937. (1,Jan), 223-262.

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